Question

The effects of a weight loss drug are standard normally distributed where negative data values represent weight loss. What is the probability a person loses 1.5 pounds or more? (round your answer to the nearest thousandth)My math:Weight loss of 1.5lbs, Z-score = -1.5Probability a person loses 1.5+ lbs = P(x > -1.5)1 – P(X > -1.5)1 - 0.0668 = 0.9332, or 0.932 (this answer was labeled as WRONG)Comment from online quiz: What is the z-score? How can you find the probability from the z-table?Please help clarify what I did wrong. Thanks! -Michelle

Answer 1

`P(X\leq -1.5) = P(X < -1.5)=P(Z<-1.5)=0.067`

Explanation:

For this case we know that our random variable X="weight loss or gain" is distributed on this way:

`X \sim N (\mu =0, \sigma=1)`

And we want the probability a person loses 1.5 pounds or more. If we interpret this an individual person losses 1.5 pounds or more if our random variable is equal or lower than 1.5. That means this:

`P(X\leq -1.5) = P(X < -1.5)=P(Z<-1.5)`

And for this case we can use the normal standard distribution or excel with the following code:

"=NORM.DIST(-1.5,0,1,TRUE)"

And we got:

`P(X\leq -1.5) = P(X < -1.5)=P(Z<-1.5)=0.067`

We need to remember that if the negative number decrease on the weight loss we are increasing the loss. For this reason we just need to find P(X<-1.5).